Analysis for SSFA project: Two factor model

Table of contents

  1. Used packages
  2. Global settings
  3. Load data
  4. Model specification
  5. Inference
    1. epLsar
    2. Asfc
    3. Smfc
    4. HAsfc9
    5. HAsfc81
  6. Summary

Used packages

Global settings

Output

Plotting

Computing

Load data

Show that everything is correct:

x1 indicates the software used, x2 indicates the treatment applied.

Model specification

Inference

epLsar

Verify model settings

Check prior choice

Prior choice is as intended: Broad over the data range.

Sampling

Save for later comparison

Check sampling

Posterior predictive distribution

Level plots

Posterior and contrasts

Verify model settings

Check prior choice

Sampling

Check sampling

Posterior predictive distribution

Compare prior and posterior for model parameters

Posterior and contrasts

Asfc

Verify model settings

Check prior choice

Prior choice is as intended: Broad over the data range.

Sampling

Check sampling

Posterior predictive distribution

Compare prior and posterior for model parameters

Posterior and contrasts

Smfc

Verify model settings

Check prior choice

Prior choice is as intended: Broad over the data range.

Sampling

Analysis stopped here because sampling did not converge. As the plot shows, some data points are very far away from the others, which would require the analysis to be based on more heavy-tailed distributions.

HAsfc9

Verify model settings

Check prior choice

Prior choice is as intended: Broad over the data range.

Sampling

Check sampling

Posterior predictive distribution

Compare prior and posterior for model parameters

Posterior and contrasts

HAsfc81

Verify model settings

Check prior choice

Prior choice is as intended: Broad over the data range.

Sampling

Check sampling

Posterior predictive distribution

Compare prior and posterior for model parameters

Posterior and contrasts

Bimodal distribution in contrast plots of HAsfc81

For e.g. the pair Clover+Dust vs. Clover shows an unexpected bimodal distribution of the contrast. We now examine the traces carefully to exclude errors in the sampling:
Get the traces on ConfoMap of the interactions

Get the traces of the treatments:

Look at all the pairs

Let's have that of the differences again

We see two sets that are distributed along parallel lines in the scatter plot. This means that the model estimates two subsets of possible differences.
However, when looking at the raw data at 'R_analysis/plots/SSFA_Sheeps_plot.pdf' one can see that the distribution of values for HAsfc81 on Clover (Sheep) measured by ConfoMap appear to have a bimodal distribution.
Thus, in combination with the chosen uninformative priors, the model correctly describes the distribution as bimodal.
In summary, we see no issue with the modeling and sampling.

Summary

Set the surface parameters for every treatment dataframe:

Show the treatment pairs and surface parameters where the softwares differ

Write out